A Brief History of the NFL Passer Rating System

Philip Rivers of the San Diego Chargers had a phenomenal season in 2008.  Or did he?  According to the NFL's passer rating system, Rivers' season, where he completed 312 passes out of 478 attempted, threw for 4,009 yards, and 34 touchdowns against 11 interceptions resulted in a passer rating of 105.5.  That's great, right?  Before we answer that question, we'll need to answer a few more questions.

How do the statistics 312 for 478, with 4,009 yards, 34 touchdowns and 11 interceptions translate to a rating of 105.5?

What does having a rating of 105.5 mean?

Where does Rivers' season rank all-time?

How has the average NFL passer rating changed over time, and how does that affect how we look at Rivers' season?

The NFL began keeping statistics in 1932.  The NFL has used various methods to determine the "best" passer in the years since.  According to the Pro Football Hall of Fame, the following is a chronology and description of the different methods used:

1932-1937: Total yards passing

1938-1940: Percentage of completions

1941-1948: Inverse ranking system of the following categories: completions, percentage of completions, total yards, total TD passes, number of interceptions, and percentage of interceptions

1949: The same formula used from 1941-1948 except the number of interceptions were dropped from the equation

1950-1959: Average yards gained per pass with a minimum of 100 attempts needed to qualify

1960-1961: Inverse ranking system based on six categories: total completions, total yards, total TD passes, percentage of completions, percentage of interceptions, average gain per attempt with the principle established of at least 10 attempts per game to qualify

1962-1971: Inverse ranking system based on four categories: percentage of completions, total touchdown passes, percentage of interceptions, average gain per attempt

1972: Same system used from 1962-1971 except that the percentage of touchdown passes was substituted for total touchdown passes

1973 to present:  See below.

Current NFL Passer Rating System:

The passer rating system used by the NFL has been in place since 1973.  In 1971, after the merger, then-commissioner Pete Rozelle wanted to implement a standardized set of statistics, including a standard measure of passing performance.  As the description on the Hall of Fame site suggests, this is a measure of a quarterback's passing effectiveness, not a measure of how good a quarterback is.  Rozelle called upon Don Smith, then an executive with the Hall of Fame, to work with the league's official statistician, the Elias Sports Bureau, to develop a new standard.  

One of the problems with the standard that existed at the time, was that you didn't know where you stood until all the teams' quarterbacks had finished playing, as it was a relative ranking system.  In addition, there wasn't a convenient way to compare a performance in a given year to that of another.

Don liked the use of the combination of statistics - in other words, the completion percentage, the yardage per attempt, the touchdown percentage and interception percentage.  He had to figure out how to use all four in some manner that would make sense.

Working with the Elias Sports Bureau, he studied passing statistics for each of the four categories from the decade before - the sixties.  After much study and thought, he devised a system whereby, for each of the four statistical measures, he would convert that particular measure to a "score" between 0 and 2.  A score of 0 would indicate poor performance, a score of 1.00 would indicate "average" performance, and a score of 2.00 would indicate "superior" performance.  With truly exceptional performance, it was possible to exceed a score of 2.00.  He arbitrarily chose the maximum score to be 2.375.  

He decided that an "average" performance across all four categories, that is, a score of 1.00 for each of the four measures, should be a rating of 66.7.  Under this new rating system, it would be possible for a rating to exceed 100.0, but, he theorized that those instances would be rare.

(Note:  I took a lot of this history from an article written by Don Steinberg, published in Slate magazine in 2001 - see here for the full article)

In summary then, this is how we end up with the current NFL passer rating system:  we take four components of passing, convert each component, using league averages from the 1960's, to a score with a minimum of 0.000 and a maximum of 2.375, combine these scores by adding them, and convert to a rating system that has 66.7 as the "average".

Here's the math that does this:

Q = [ ( J + K + L + M ) * 100 ] / 6

where,

Q = Passer Rating

J = max [ min ( C, 2.375 ), 0 ]

K = max [ min ( Y, 2.375 ), 0 ]

L = max [ min ( T, 2.375 ), 0 ]

M = max [ min ( I, 2.375 ), 0 ]

and where,

C = [ ( Completions / Attempts ) * 100 - k1 ] / 20

Y = [ ( Yards / Attempts ) - k2 ] / 4

T = [ ( Touchdowns / Attempts ) * k3 ] * 20

I = 2.375 - [ ( Interceptions / Attempts ) * k4 ] * 25

and where,

k1 = 30

k2 = 3

k3 = 1

k4 = 1

In the first formula, you can easily see where if J = K = L = M = 1.000, the passer rating formula would yield Q = 66.7.  In order to get J = K = L = M = 1.000, certain "transformations" were needed to each of the passing statistics to convert the averages to a score of 1.000.  The transformations for each are shown as C, Y, T, and I, and, more specifically, k1, k2, k3 and k4.  The figures for k1-k4 were derived using league statistics from the 1960's, and to make it somewhat easier, rounded.  If you looked at data from 1960-1969, you get the following actual values for k1-k4:

k1 = 31.70

k2 = 3.24

k3 = 0.96

k4 = 0.99

The table below shows, for each NFL season from 1940-2008, how the averages, or, more precisely, the "scores" for those averages have changed from year to year (for a graphical illustration see my previous post on the subject here).  For example, you can see that the average score for "J", in 2008 was 1.550, reflecting the fact that the "C" component, or, completions per attempt, for the average NFL quarterback was 61.0%.  Compare this to the average score for "J" in 1968 of 1.079, reflecting the "C" component, or completions per attempt of that time of 51.6%.  This is what happens when the transformations do not change over time, even when the actual game itself has undergone many transformations.  If one wanted to keep everything in balance from year to year in the passer rating formula, in other words, to keep J = K = L = M = 1.000 for every year, then one would have to change the values of k1 - k4 every year.  I have done that in the table below.

You can use these different k values every year to "adjust" the passer rating formula, so that you can make meaningful comparisons from year to year.  If you didn't do that, and simply compared a quarterback rating from one year to the next, you wouldn't get an appropriate comparison, for the simple reason that the four components would be "out of balance".  

While it was never Don Smith's intention to have a relative measure of performance - he wanted performance as measured relative to a fixed standard, that "fixed" standard has changed, and will continue to change over time.  One way to minimize the effect of these changes is to look at a given performance in a given year to that season's average, using the standard deviation as a measuring stick.  The other way, is to simply "adjust" the standard to reflect the averages for that year.  In a previous post, I discussed the former method.  In this, I am obviously discussing the latter.

This discussion is only to put Rivers' 2008 season in perspective.  It is not intended as passing judgment on the NFL passer rating system.  I have, in previous posts (see here and here) discussed why I do not like the system.  In a post in the future, I'll elaborate further on why I think the NFL's passer rating system should be revised.

The table below shows the 75 greatest seasons in the NFL, both in terms of the current NFL passer rating system, and using an "adjusted" passer rating system, going through the transformations as I have described above.  You can see that, using the current system, that Rivers' 2008 ranks as 13th best all-time.  Using an "adjusted" passer rating system, however, results in a ranking of 60th best all-time.  If we used the previously mentioned standard deviations from mean measurement, it would rank as the 16th best all-time.

We still have some unfinished business:

How does Rivers' stats translate to a rating of 105.5?

He completed 312 of 478 passes, or, a completion percentage of 65.3% - using k1 = 30, and Comp/Att = 0.653 in the formulas above, yields a J value of 1.764

He threw for 4,009 yards, or, yards per attempt of 8.4 - using k2 = 2, and Yards/Att of 8.4, we get a value for K of 1.347

He threw 34 TDs, or, TD/Att of 7.1% - using k3 = 1, and TD/Att = 0.071, we get a value for L of 1.423

He threw 11 INTs, or, INT/Att of 2.3% - using k4 = 1, and INT/Att - 0.023, we get a value for M of 1.800

Combining all, we get

Q = ( J + K + L + M ) * 100 / 6, or

Q = ( 1.764 + 1.347 + 1.423 + 1.800 ) * 100 / 6 = 105.5

There is no doubt that, whether we use the current NFL passer rating system, an "adjusted" passer rating system with different transformations for different years, or, the current system, but adjusted by looking at standard deviations from the mean, that Rivers' 2008 season was quite remarkable.  

Whether the passer rating system is an accurate reflection of a passer's ability is a completely different question altogether.  We shall, over time, address this question.

Anybody Looking for a Good QB?

Available:  Experienced quarterback with an accurate arm with ability to make immediate contributions to team; Ideally, would like to start, but not a requirement; may be perfect as back-up; durability maybe an issue.

I am referring of course to Jeff Garcia, released today by the Tampa Bay Buccaneers.  I am personally a big fan of Garcia, because I believe he is underrated, and his achievements on the field have gone relatively unnoticed.

Let's take a look.

He began his NFL career in San Francisco in 1999, replacing not one, but two back-to-back Hall of Famers, and arguably the two greatest passers of all-time, Joe Montana and Steve Young.  There was no way Jeff could live up to those lofty expectations.  However, he did perform very well, as the table and chart below shows.  While he may not have performed at Joe Montana and Steve Young levels, his years in San Francisco were very productive.  After a sub-par year in 2003, he bounced around for three years, first as a starter in Cleveland (2004), then as a back-up in Detroit (2005) and Philly (2006).  He finished the 2006 season as the starter in Philadelphia for the last 6 games after Donovan McNabb got injured.  He showed that he could still play, and Tampa Bay, in need of a quarterback following an injury to Chris Simms, picked him up.  He did well above average each of 2007 and 2008, as you can see from the table and charts (he doesn't show up in the charts in the years 2004-2006 since he didn't attempt enough passes to qualify).  

Now, Tampa Bay, deciding to turn to the youth movement, have invested in Luke McCown, and, have deemed Garcia expendable.  

Garcia has been a very accurate as a passer throughout his career.  In a previous post, I discussed interceptions at length.  His 2007 season ranks 18th all-time (see Exhibit 3 in this post) in interceptions per attempt, in terms of standard deviations from the mean (his 2008 season ranks 118th, out of the 1,451 seasons in the database since 1940).  As a career passer, he ranks 12th all-time (see Exhibit 6 in this post).  By not throwing interceptions, he will help your team win.

I believe that Garcia has a couple of good years still left in him, if not as a starter, as a back-up.  His durability has been an issue the past two seasons, and hence, might be a liability as the starter.  

So who might be worthwhile candidates?

The following charts show, for each of 2007 and 2008, how a team's passing game stacked up in terms of standard deviations from the mean.  It's no coincidence that teams that were above average won more games than they lost, and teams that were below average lost more games than they won.  The charts show how the teams did both in terms of NFL passer rating and CMI.  Note that Garcia averaged 0.53 standard deviations above average in terms of NFL passer rating for the past two seasons, and averaged 1.23 standard deviations above average in terms of CMI.

To see which teams should be looking to get Garcia, let's start at the bottom, and move our way up.

Cleveland Browns - They have two young quarterbacks, Derek Anderson and Brady Quinn, both coming off season-ending injuries, that will compete for the starting job.  Not a candidate.  Look for another miserable year in Cleveland.

St Louis Rams - Marc Bulger is the starter, and for now at least, another soon-to-be 39 year-old - Trent Green, is the back-up.  Not a candidate.  By the way, what's happened to Bulger?  Will 2009 be more like his first few years, or his last two?  I suspect the latter.  Another long year in St Louis.

Oakland Raiders - Paying a lot of money for JaMarcus Russell.  They've also got Andrew Walter, Marques Tuiasosopo, and they just picked up Bruce Gradkowski off waivers.  I haven't a clue what the Raiders are doing, and I don't think the Raiders do either.  Not a candidate.  Perhaps we'll start paying attention when Al Davis passes away.

San Francisco Forty Niners - They're not sure who their starting quarterback is.  Shaun Hill?  J.T. O'Sullivan?  Alex Smith?  The niners maybe a candidate.  Garcia played here, and is originally from close-by Gilroy.

Detroit Lions - Daunte Culpepper is the starter.  Or is it Dan Orlovsky?  Didn't seem to matter in 2008, as they went 0-16.  If I was GM, I'd replace Culpepper with Garcia, and draft a quarterback.  But that's just me.  Garcia may not want to go here, but that's a different matter altogeher.

Chicago Bears - Kyle Orton is the starter, and Rex Grossman is the back-up.  Neither of whom are very good.  I would think that Garcia would be an excellent choice to be a back-up here.

Kansas City Chiefs - Tyler Thigpen is the starter.  Previous starter Damon Huard is the back-up.  Garcia could be a potential back-up here.

Cincinnati Bengals - Ryan Fitzpatrick finished the year as the starter, having replaced the injured Carson Palmer.  Not a candidate.

Of the remaining teams, perhaps the Minnesota Vikings might be interested.  Gus Frerotte is simply not a good option.  Maybe they'll lure Brett Favre out of retirement!  The NY Jets might be an option for Garcia as well.  Most likely, Kellen Clemens will be the starter, but Garcia could be a viable back-up here.  

So these are teams that should be interested in Garcia.  We'll wait and see where he actually ends up.  

Brett Favre - Best Ever?

Brett Favre retired earlier this week.

He played in the NFL for 18 years. He set numerous NFL records during the course of his career. The most impressive has to be the fact that, as a quarterback, he started a record 269 consecutive regular season games. Peyton Manning is second on the list, his streak currently standing at 176 games. Third on the list is Ron Jaworski, his streak having ended at 116 games. Tom Brady is next on the list, but his streak ended in the first game of last season at 110 games. Peyton Manning needs another 94 games - he would have to start every single game through the 14th game of the 2014 season to break Favre's record. In addition to the four mentioned above, only two other quarterbacks in history - Joe Ferguson (107 games), and Dan Marino (95 games) have started that many games consecutively. I suspect Favre's record will never be broken.



People are fascinated with Favre. Many consider him to be among the all-time greatest to ever play the game. Some consider him the greatest ever. I do not belong to either group.


The media loved Favre. And vice versa. He never met a camera he didn't like, always seeking an opportunity to get into the limelight (of course, the media loved that). He also seemed intensely competitive, and the combination is what I believe led him to his unfortunate decision to come back for one more season in 2008.


Let's start from the beginning.


In 1991, the Atlanta Falcons took Favre in the second round of the draft. With Chris Miller as their starting QB, in 1992, the Falcons traded Favre to Green Bay. Favre started the season as the back-up to the 'Magic Man', Don Majkowski. In the third game of the season, against the Cincinnati Bengals, he replaced the injured Majkowski in the first quarter. With 13 seconds left, he threw a 35-yard touchdown that helped the Packers come-from-behind to win 24-23. He started the next game against the Steelers, a game the Packers won. The rest, as they say, is history, as he started every game for the Packers until his trade to the Jets following the 2007 season (for a detailed history of, or, more aptly, a tribute to Favre, see here).


The table below shows how Favre did each year.



Before we go on, some explanations.


In order to be able to truly compare Brett Favre to other quarterbacks so that we can properly gauge his place in history, we can't simply look at the NFL's passer rating system. First, we know that the average NFL passer rating in the NFL has been increasing over time. So, by simply using the NFL's passer rating system, the more recent quarterbacks would appear to have done better than quarterbacks from earlier years (see here and here for evidence). Second, we have to agree that the NFL's passer rating system is an accurate, if not adequate measure of a quarterback's performance. I have previously introduced a metric, CMI, which I believe is a better, if not more understandable measure of performance. CMI, however, also has the same bias as the passer rating system. One way to adjust for, and remove the bias favoring more recent quarterbacks is to look at each year's performance for each quarterback, and relate that to the average performance that year. The measure that we use is the standard deviation. I have discussed previously how using this measure tends to "normalize" performances across years. In other words, when a given year's performance by a particular quarterback is "normalized" to the average for that year, and we do that for every year, we can very easily see how that particular performance compares to other performances across years. Since CMI is very similar to the passer rating system, when using standard deviations, it shouldn't really matter whether we use CMI or the NFL passer rating system (there will be differences, and, I often include both so that you can see the differences). The two graphs below show how using either the "normalized" NFL's passer rating system or "normalized" CMI as measures compare to a standard normal curve with 1,451 observations (that's how many qualified quarterback seasons there have been over the past 69 years).



Ok, so back to the table.


Favre had a "pretty good", or, "above average" first year in 1992. Using the NFL passer rating, he finished 0.57 standard deviations above the average that year. Using a standard normal curve, that would mean between the 71st and 72nd percentiles. If we used CMI as the standard, then his performance that year, 1.24 standard deviations above the mean, would place him between the 89th and 90th percentiles.


He followed that with a sub-par year in 1993, finishing between the 30th and 31st percentiles according to the NFL passer rating system, or between the 35th and 36th percentiles using CMI. Then followed several "above average" to "very good" years (1994-1998), depending on your perspective, followed by a couple of mediocre years (1999-2000), followed by four above average years (2001-2004), followed by his two worst years (2005-2006). He finished his Green Bay tenure with an "above average" year in 2007.


He should have taken the opportunity to retire then.


His last year, his first full season not with Green Bay, was "below average". So he finished his career with 3 "below average" years out of 4. Perhaps the Packers brain trust was on to something when they decided that Aaron Rodgers was their future at the end of the 2007 season.


The two graphical illustrations below show each of Favre's seasons in terms of standard deviations from the mean. In case you haven't noticed, as much as I love statistics, I find that graphs are better way to illustrate a point than a table of statistical measures. I show the CMI graph first and the graph based on NFL passer rating next, for reasons that will become plainly apparent when you read on.





Ok, so until now, we've been looking at Brett Favre's career in a bit of a vacuum. Yes, we have compared his performances to an average, and yes, we have tried to put it into historical perspective, but I haven't given you any 'perspective'.


First, let's compare Brett Favre's career to some individual careers. The biggest problem we face in comparing Favre's career to any other individual career, is obviously the length of his career. There have been only 5 individuals who have thrown enough passes to qualify in at least 15 different seasons. Those are Fran Tarkenton (18 years), Brett Favre (17 years), Dan Marino (16 years), John Elway (16 years), and Johnny Unitas (15 years). So how does Favre's "picture" compare to these quarterbacks, all of whom are in the Hall of Fame?


Fran Tarkenton - a picture of "excellence". With a couple of exceptions, Tarkenton exceeded his peers consistently for a very long time. Quite remarkable. Without question, Favre's picture does not resemble that of Tarkenton.


Dan Marino - Marino was "above average" for many of his years, tailing off towards the end of his career. He was "very good" very early in his career. He really didn't have a "bad" year until his last, and wisely decided to hang it up after that. Although closer in resemblance, Marino's picture still looks better Favre's overall.


John Elway - Elway underperformed his peers much of his early career, exceeding the average in only two of his first ten years. He then was "above average", or even "very good" his last six years. He went out on top, having retired following the Broncos having won back-to-back Super Bowls (Super Bowl XXXII and Super Bowl XXXIII). I think it's safe to suggest that Favre's picture looks better than Elway's.


Johnny Unitas - In my opinion, Favre's picture most closely resembles that of Johnny Unitas. They both started out well, had a couple of mediocre years, then had several years where they outperformed their peers, and ended their careers with a few sub-par years.



What if we compared Favre's average performance (in other words, average each of his year's performance in terms of standard deviations), to other players? Well, over his career, in terms of NFL passer rating, Favre averaged 0.42 standard deviations above the mean (0.26 when looking at CMI). Tarkenton averaged 0.65, Marino averaged 0.63, Elway averaged 0.06, and Unitas averaged 0.51 standard deviations above the mean.


Let's expand the comparison list to players who qualified in at least 10 different seasons. 41 different quarterbacks make that list. The two graphs below illustrate where Favre ranks on those lists.



The same graph as above, except looking at it Using CMI as the measure of performance.




Looking at his career statistically, it is hard to make the argument that he belongs in the truly elite group of all-time quarterbacks - those that would be ranked in the top 3 or top 5 all time. I think it is fair to suggest that Favre has had a very good career. It was certainly a lengthy one, and, in that regard, it was exceptional. But as far as his actual performance on the field, there isn't a measure, or set of measures, that suggest that it was exceptional.


People will suggest that he holds the all-time record for yards, or touchdowns, for example. But that is merely a function of his longevity, just as much as he holds the record for interceptions thrown, all-time.


I also don't discuss measures frequently used as evidence of greatness. MVP awards, for example - these are popularity contests more than a reflection of outstanding statistics or an individual's value to a team (the NFL MVP award is given by the Associated Press). Pro-bowl selections for example are another popularity contest - just look at who got selected this past year in the AFC. Another measure frequently used is Super Bowls. Dan Marino didn't win any Super Bowls. Trent Dilfer won a Super Bowl. Winning percentage is also frequently used - last time I looked, a quarterback doesn't play defense, return kicks or punts, or kick field goals. These pieces of evidence would never enter any serious discussion in terms of statistical evaluation.


My eventual goal is to identify the greatest passer of all time. I will use several statistical measures, many of which are mentioned in this post, to identify the most worthy candidates for consideration. As far as my research is concerned so far, Favre would not make that list. There are several other quarterbacks, not mentioned in this post, nor even displayed in either of the last two graphs that would make more worthy candidates, but that is for a different article.

The Importance of Interceptions (or lack thereof)

I have spent quite a bit of time lately talking about interceptions.  In case you have any doubt that an interception can make a difference you got that answer on Super Bowl Sunday.  In probably one of the greatest plays in Super Bowl history (until the catch by Santonio Holmes with 35 seconds left that gave the Steelers a come-from behind victory), with Arizona on the Pittsburgh 1 yard line, first and goal, and 18 seconds left in the first half, the Steelers' James Harrison picked off Arizona's Kurt Warner and returned it all the way for a touchdown as time expired.  This was, in effect, a 13-point play, as Arizona's expected points at the Pittsburgh 1 was about 6 points.  Brian Burke, who I've highlighted before, has an excellent post on the subject on his site at advancednflstats.com.   

Take a look at the graph below.  The blue line (on the left scale) shows the league average QB passer rating (for those QBs who thew enough passes during the season to qualify) by year since 1940.  As you know, the NFL's QB passer rating formula has four components - completion percentage, yards per attempt, touchdown percentage, and interception percentage (see my previous posts on the subject here and here).  When it was designed in 1973, the formula used the 1972 season as a "base", and hence created adjustments to each component, such that the average would be a score of 1.00 for each component, resulting in a passer rating for 66.7 for a quarterback who had average statistics in each of the four categories.  The actual calculations for each of the four components in 1972 yielded the following four figures - 1.085, 0.954, 0.897, and 1.043, respectively, which in turn yielded the average quarterback passer rating of 66.3 (the figure for the qualified leaders turns out only slightly higher - 67.9).  Back then, each of the four components were essentially balanced.

Today, it's a different story.  If the system was balanced, then we would expect the interceptions component to make up about 25% of the quarterback passer rating score.  Looking at the graph again, and this time looking at the red line (on the right scale) shows how much the interceptions component influences the league's quarterback rating system.  It hasn't been below 30% since 1983, and the last time it was "around" 25% was actually 1971.  The point is that the NFL passer rating system is not what it used to be, and interceptions are the leading weight in today's NFL passer rating system.

Let's take a look at another example.  Tom Brady's record-breaking 2007 season.  That year, Brady completed 398 of 578 passes, for 4,806 yards, and threw for 50 touchdowns while only throwing 8 interceptions.  His passer rating that year - 117.2, is second only to Peyton Manning's all-time best 121.1 in 2004.  Most people will remember the 50 touchdowns that Brady threw.  Impressive as it was, it wasn't that impressive (I'll have a post later on this subject).  Most people will not remember that he only threw 8 interceptions in 578 attempts.  That ranks as 14th best all-time in terms of single-season interception percentage (see Exhibit 2), and, it accounted for 29% of his quarterback passer rating that year (his touchdowns accounted for 25%).

There are 7 exhibits on interceptions attached to this post.   Note that for all exhibits, I only considered those passers in any given year that threw enough passes to qualify - in other words, if a quarterback threw 20 passes during a season, that would not be enough to qualify him.  On the nfl.com site, the minimum qualification standard is 14 passes per game (so, for the 2008 season, the standard would be 14 * 16 = 224 passes).  The NFL uses this standard EVERY year.  

I think this universal standard is inappropriate.  Using this method for example, only three passers qualified in 1940.  The 14 passes comes from the fact that during the 50's, 60's and 70's, the average number of passes attempted by a team during a game was about 28.  Of course, we all know that this has changed over time.  The average number of passes attempted in a game by a team was 32.3 in 2008.  It has been below 30.0 once since 1979.  

The standards that I use varies by year, and reflects the average # of passes attempted during these years.  Here are the standards:

1940-1946 - 6.5

1947-1960 - 11.0

1961-1969 - 14.0

1970-1977 - 12.0

1978-1994 - 15.0

1995-2008 - 16.0

Using these standards, I get 1,451 quarterbacks in my database, with a low of 9 quarterbacks qualifying in each of 1941 and 1943, and a high of 32 quarterbacks qualifying in each of 1999 and 2005.  For 2008, I had 30 quarterbacks in my qualified database, whereas the NFL.com has 32.  So, not a big difference in recent years.  I just think that applying a universal standard across all these years is silly, especially when the game has changed so much.

In any case, now that we got the some of the technical stuff out of the way, here are the 7 exhibits:

Exhibit 1 - Chronological list of NFL leader (lowest) in interception percentage

Exhibit 2 - Best seasons in terms of interception percentage

Exhibit 3 - Best seasons in terms of standard deviations from the mean

Exhibit 4 - Worst seasons in terms of standard deviations from the mean

Exhibit 5 - Best (lowest) career interception rate (minimum of 1,000 passes attempted)

Exhibit 6 - Best career interception rate relative to league average

Exhibit 7 - Worst (highest) career interception rate relative to league average

Exhibit 1 - Chronological list:

Nothing spectacular here, it's simply each year's best.  I observe a few things: 

Clearly, the average interception rate has been decreasing every decade.  

The best quarterbacks in a given year seem to be around 1.8 standard deviations better than the average.

Slinging Sammy Baugh led the league 4 out of 6 years during the period from 1942 to 1947 - the only quarterback to have led the league on 4 separate occasions.  

6 quarterbacks - Bart Starr, Bobby Thomason, Charlie Conerly, Ken Anderson, Ken O'Brien, and Roger Staubach have led the league on 3 different occasions.

5 quarterbacks led the league in consecutive seasons - Sammy Baugh, Bobby Thomason, Milt Plum, Ken Anderson and Ken O'Brien.

Only 2 quarterbacks in history, Steve DeBerg in 1990 (0.90%), and David Garrard in 2007 (0.92%) completed a season where less than 1 percentage of their attempted passes were intercepted (this is not entirely evident by looking at Exhibit 1, but can be confirmed by Exhibit 2).  What's most unusual about DeBerg's performance that year was the fact that of the four interceptions he threw during the season, three of them were in one game!  In other words, he threw 1 INT the rest of the season.  Let's take a look at Exhibit 2.

Exhibit 2 - Best seasons in terms of interception percentage:

So indeed, only 2 quarterbacks have had seasons with fewer than 1% interceptions.  The list below is the kind of list that would show up in a record book.  

You'll see, for example, that Jason Campbell's 2008 season ranks in the top 5 all-time, and 2 other quarterbacks in 2008, Chad Pennington and Jeff Garcia, also had noteworthy seasons, with both finishing in the Top 30 all-time.  

If you look carefully, you'll notice that the list is dominated by quarterbacks in the past 2 decades.  Of the Top 50, 45 have occurred since 1990.  21 last decade and 24 this decade.  The 5 seasons in the top 50 not to have occurred in the last 19 years are Steve Bartkowski's 1983 season (#3), Bart Starr's 1966 and 1964 seasons, respectively (#7 and #18), and Ken O'Brien's 1985 and 1988 season's respectively (#36 and #38).  

So, what are we saying?  Are we saying that quarterbacks prior to 1990 were not very good?  No, not at all.  The league has changed.  From Exhibit 1, you can see that the average interception rate has been decreasing every decade.  So, we simply can't just compare a quarterback from one decade to another.  That's where Exhibit 3 comes in.  Let's take a look at that.

Exhibit 3 - Best seasons - Interceptions percentage, ranked by how different the particular season was compared to the mean, using the standard deviation as the measuring stick:

Wow, what a difference.  You can quickly see that this is a much better representation of the past 7 decades.

1940's - 3

1950's - 2

1960's - 10

1970's - 9

1980's - 7

1990's - 6

2000's - 13

Look at Bart Starr!  Ranked twice in the Top 5, and 3 times in the Top 25.  

And, this measure doesn't discount Steve DeBerg's and David Garrard's great seasons - they're both still in the Top 5.  But it does give one a bit more perspective.  In other words, this suggests that Bart Starr's 1962 season (which ranks #430 in absolute terms), when compared to everyone else's performance during that season, was better than David Garrard's performance, when compared to how all the other quarterbacks did in 2007.

Now for a little math.  Why are we using standard deviation as a measure of separation?  And why does using it make comparing quarterbacks across years more meaningful?  

A non-technical definition of the standard deviation is that it is a measure of the dispersion of a set of data around the average.  By dispersion we mean spread.  Knowing the average of the data, and knowing how spread the data is, we can try to determine how likely a given observed value is.  We can use this data to compare different data sets, and relate them to one another.   So for example, in a data set where the average is 5, and the standard deviation is 2, an observation of 8, would mean 1.5 standard deviations ((8-5)/2 = 1.5) above the the mean.  In a data set where the average was 7, and the standard deviation was 4, a value of 13 would also be 1.5 standard deviations from the mean.   You can now see why the use of a standard deviation could be useful in comparing different sets of data.  

As you can see from Exhibit 1, the league average interception rate has been changing over time.  In addition, while I have not shown it explicitly, the standard deviation around the mean has also been changing.  As a matter of fact, in the early 1940's, the standard deviations were quite high because there were fewer players involved, the number of attempted passes were fewer, and arguably the talent pool was not as great (i.e. passing was a fairly new concept).  

By relating a given observation of an interception rate in 1943 to the mean interception rate that year, and the standard deviation of interception rate that year, one can then compare that particular observation to an observation of an interception rate in 2003, by its relationship to the mean and standard deviation of interception rates in 2003.  If one assumes, in particular,  that in any given year, that all observations about the mean are distributed normally (i.e. a "bell-shaped" curve), then the comparisons become that much more meaningful.  For example we know that in a standard bell-curve, that approximately 68% of the observations will fall into a band +/- 1 standard deviation from the mean, and approximately 95% of observations will fall into a band +/- 2 standard deviations from the mean.  Also, if, after relating the observations in each year to each year's mean and standard deviation, one aggregates the data across all years (since the data has been "normalized" to the same scale - a number in relation to a mean and standard deviation; in the example earlier, the observation of 8 in the first data set has the same value on a normalized basis as the observation of 13 in the second data set - 1.5), then the aggregated data should look like a standard normal curve, with a mean of 0, and a standard deviation of 1.  

Well, I went through the trouble of doing that, and guess what - that is exactly what the looks like.  All 1,451 qualified passers over the 69 years from 1940 to 2008 were analyzed in this manner, and the result is in the graphical illustration below.  The average for the entire data set is -0.06 (close to 0), and the standard deviation is 1.00!  Also, it turns out that 69% of the observations are within +/- 1 standard deviation, and 96% are within +/- 2 standard deviations.  Quite a remarkable achievement!  I've graphed a standard normal distribution as well, so that you can see for yourself how close the actual data is to the theoretical curve.

Exhibit 4 - Same as Exhibit 3, except ranks the worst seasons:

Terry Bradshaw's 1970 rookie season ranks as the all-time worst.  And Vinny Testaverde's 1998 campaign is not that far behind.  Although Testaverde's rookie season was 1987, he didn't "get exposed" until 1988.  Most recently, Gus Frerotte's 2008 campaign was an absolute disaster.  There's some names on the list that I would not have expected to see (let's face it, these are the 50 worst performances over the past 69 years - 1,451 quarterback seasons) - names like Favre and Aikman, along with the aforementioned Bradshaw.  What was even more surprising to me was that they each showed up not once, but twice!

So now you've seen the best and the worst seasons.  How about careers?  Let's take a look at Exhibit 5.

Exhibit 5 - Lowest career interception rate - absolute figures - with a minimum of 1,000 passes attempted:

For reasons I discussed above, I don't like this list that much, as it is biased towards the more recent years.  But, since people like looking at these types of lists, I have included it.  Exhibits 6 (best) and 7 (worst) reorder the data after a player's career has been compared to the average during their career.

Exhibits 6 (best/lowest) and 7 (worst/highest) - career interception rate relative to league average during the same time:

First question is: why, after the long dissertation about standard deviations, am I not using that as the measuring stick?  Simple answer - it's difficult!  It was a relatively simply exercise to calculate standard deviations for each year.  And it's not that difficult to do it for a given set of consecutive years.  Where it becomes increasingly difficult is to do it for every combination of multiple years, over a 69-year period.  At some point before the 2009 NFL season, I'll have it done.  That will be a better reflection of who had good or bad careers, but, in the meantime, this will have to suffice.  It's the next best thing.  It is most certainly better than the absolute comparison shown in Exhibit 5.

Ok, on to a few observations.

Exhibit 6 is a who's who of quarterbacks in football history.  Taking out the 13 players who are either currently playing, or who have retired in the past five years (i.e. not Hall of Fame eligible), 14 of the remaining 37 are in the Hall of Fame.  Let's look at it another way.  There are 27 quarterbacks who are in the Hall of Fame, who played football post 1940.  And two of them, Arnie Herber, and Clarence (Ace) Parker, played much of their careers before 1940.  Of the remaining 25, 14 show up in Exhibit 6.  

Who are the 14?

Joe Montana (#3)

Roger Staubach (#9)

Steve Young (#14)

Sammy Baugh (#19)

Fran Tarkenton (#20)

Bart Starr (#22)

Sonny Jurgensen (#23)

Otto Graham (#32)

Dan Marino (#33)

Sid Luckman (#37)

John Elway (#39)

Len Dawson (#42)

Johnny Unitas (#46)

Norm Van Brocklin (#50)

And 2 more, Y.A. Tittle (#53), and Troy Aikman (#55) just missed being in the Top 50.  Not a bad list.

What about Exhibit 7?  3 Hall of Famers, Joe Namath, George Blanda, and Terry Bradshaw are in the worst 50 all-time, in terms of their career interception percentage as it relates to the league average during the time that they played.